The government, however, said it was in full control of the town, the capital of Upper Nile State in the northeast and one of South Sudan's main oil-producing areas.
"The whole of Malakal is under the control of our forces. It was cleared yesterday evening," said Moses Ruai Lat, spokesman for the Unity State Military Interim Government -- or the rebels loyal to Machar and opposed to President Salva Kiir.
"All those forces who are loyal to the president have been cleared and the former governor of Upper Nile, Simon Kun Poch, is on the run," he told AFP.
But South Sudanese Defence Minister Kuol Manyang Juuk said the claim was "disinformation".
"The elements loyal to Riek Machar were defeated and they are no longer in Malakal. The town is under full government control," he said, adding that government troops -- the Sudan People's Liberation Army (SPLA) -- were reinforcing their presence in the town.
There was no immediate independent confirmation of which side was in control of the town, although independent sources reported heavy fighting inside the town overnight Thursday.
The fighting in South Sudan started on December 15 after Kiir accused Machar, whom he sacked in July, of attempting a coup.
Machar denied this, and said the president was exploiting a clash between members of the army as a pretext to carry out a purge.
Rebel forces also control Bentiu, capital of the oil-rich Unity State, but the government says its forces are advancing on the town.
The violence in South Sudan, a fledgling oil producer which won independence from Sudan just two years ago, has left thousands dead, according to the United Nations.
Ten of thousands of civilians have also sought protection at UN bases amid a wave of ethnic violence pitting members of Kiir's Dinka tribe against Machar's Nuer community.
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